Questions tagged [heuristics]

Questions about algorithmic strategies that quickly solve a problem well most of the time, but give no guarantees.

Filter by
Sorted by
Tagged with
1
vote
1answer
127 views

Overall time complexity of Heuristical Algorithm for travelling salesman problem [TSP]

I am trying to figure out the time complexity of a heuristical algorithm used to solve the Travelling Salesman Problem in a more efficient way than by brute force, ($\theta(n!)$ or similar) The ...
1
vote
1answer
288 views

How do I compute this non terminal positions evaluation, for tic-tac-toe?

Looking at this solution on page 3 but having trouble understanding the evaluation function specifically. For non terminal positions, we use a linear evaluation function defined as Eval (...
1
vote
2answers
914 views

Heuristics & Constrain Satisfaction Problem Differences

I'm currently taking an Algorithms course, and we are covering Backtracking, CSP, and heuristics. However, I'm getting confused on exactly the differences between these terms and their applications. ...
1
vote
1answer
39 views

What is the peak in fitness landscape

I have just started reading about fitness landscapes and I couldn't understand what the peak means. What does the peak mean?
1
vote
1answer
3k views

How does the nearest insertion heuristic for TSP work?

In my theoretical computer science class and we were covering "Heuristics". In it we covered "Greedy Heuristics" for the "Vertex Cover Problem", "Interval Scheduling" and the "Traveling Salesperson ...
1
vote
1answer
548 views

If h(n) is a perfect heuristic (that is, h(n) = h*(n)), then does it imply that A* will always take linear time complexity?

That is, if h(n) = h*(n), then A* only expands nodes that lie on an optimal path to the goal. But does this imply that A* will always take a linear time in the solution length to find an optimal ...
1
vote
1answer
445 views

How to proof a heuristic?

I am not very familiar with "heuristic", so please correct me if anything said by me is wrong. Per my understanding, Algorithm is an automatic steps which guarantee to give a correct solution ...
1
vote
1answer
1k views

Sort array with minimum swaps

Given an array, I need to sort the array (if not already sorted) in either decreasing or increasing order so that number of swaps are minimized. I was thinking of first determining whether it is ...
1
vote
1answer
90 views

Search Heuristics Where the Search Space Has No Gradient

If I'm not mistaken, search heuristics rely on problems where the best answer is very close to pretty-good answers. For example, the traveling salesman problem. If there is a route which is the ...
1
vote
1answer
870 views

Monotone property of heuristic in $A^*$ algorithm

In the $A^*$ algorithm, the optimality of the path is guaranteed when the heuristic has the property of being admissible or monotone\consistent. I was able to understand the admissible property, ...
1
vote
1answer
903 views

Can heuristic methods and machine learning approaches be considered alternate methods to solve NP-Complete problems?

I was watching the videos from Skiena's Computational Biology Lectures, which is also available at youtube. In those videos, the professor made a statement that, most of the problems posed to computer ...
1
vote
1answer
496 views

Algorithm to use for a TSP variant

What type of algorithm would you suggest me to use for this problem? I want to implement an algorithm that minimize the total distance in a graph (TSP) but for only X nodes. Also, we can go as many ...
1
vote
1answer
22 views

Do we understand when metaheuristics are optimal? (gradient descent & simulated annealing in particular)

Gradient descent sometimes works better than simulated annealing and vice versa. Are there conditions under which we can prove that, given perhaps a restriction on the set of allowed algorithms, one ...
1
vote
1answer
23 views

Justification behind this heuristic in SMA*+

I'm reading the paper Enhanced Simplified Memory-bounded A Star (SMA*+). In short, the authors propose a limited-memory version of A* where we cull nodes if we are out of memory, to re-expand them ...
1
vote
1answer
20 views

How to get initial flow for TSP with missing edges

I need to solve a version of the traveling salesman problem with missing edges. I've decided to use simulated annealing. How do I generate a valid initial path effectively? I would use a greedy ...
1
vote
1answer
147 views

Improvement Heuristics for Asymmetric TSP

i have been solving the Time-Dependent Traveling Salesman Problem using an Ant Colony Optimization. Upon reading the ACO papers, there are several reminders which state that ACO performs best with ...
1
vote
1answer
202 views

consistent heuristic - does it always exist?

I am studying for an artificial inteligence class, and i have to classify the following sentence "For any search space, there is always an admissable and consistent A* heuristic". Well, i know that ...
1
vote
1answer
75 views

Movement on Labyrinth with Best First Search

I have the following labyrinth where R is the robot(the parent node), red blocks are the obstacles where the R cannot move and <...
1
vote
2answers
144 views

What is the importance of disjoint edges in k-opt algorithms?

I'm trying to implement a k-opt algorithm and I'm bogged down on a detail: the importance of choosing disjoint edges. My question: Is there any benefit to considering adjacent edges, or is the full ...
1
vote
1answer
65 views

Distribution of beans in jars to k members

Here is the problem. We have N jars. Each jar can have any number of beans. These beans have to be distributed among C children. The resulting distribution should serve two goals Now the number of ...
1
vote
1answer
680 views

How are the 1s and 0s derived by the minimax algorithm for the game called “nim”?

I'm having trouble figuring out why the 1s and 0s are where they are in this game tree for the game Nim: There is a statement in the book that explains the numbers but it's still not clear to me, In ...
1
vote
1answer
151 views

Solving an ordered knapsack problem exactly with a non linear (blackbox) evaluation function

Thanks in advance for the help. I have the following problem which, for lack of a better description, I'm referring to as the problem I've listed in the title. Specifically I have a knapsack problem ...
1
vote
1answer
137 views

Metaheuristic for NP-complete problem without exact algorithms other than brute-force

Computing Pure Nash Equilibria (PNE) is a Game Theory related problem. Deciding if there exists PNE in a given game has been shown to be NP-Complete (Gottlob et al.). I want to design a metaheuristic ...
1
vote
1answer
206 views

Numerical Boardgame — Help with with a pruning method (alpha-beta : minimax)

I'm developing a simple AI to play a boardgame which consists of N x N squares, each with a predefined value. ...
1
vote
1answer
329 views

Local search: Problem with neighborhood definition

I have question on understanding the following neighborhood relation within a local-search approximation scheme. Let $M$ be a legal matching on any bipartite graph. Let $U_k$ be the neighborhood ...
1
vote
1answer
4k views

Why is Uniform cost search called “uniform” cost search?

By this possibly good attempt to explain this, the "uniformity" in the Uniform cost search is actually the uniformity of the heuristic function. Is this explanation correct ? If yes, then don't all <...
1
vote
0answers
21 views

Is this a valid heuristic for Dots and Boxes to reduce the branching factor of the search tree?

I am implementing an AI based on the MiniMax algorithm that plays the game Dots and Boxes. I would like to reduce the branching factor of the search tree, by introducing a heuristic rule that limits ...
1
vote
0answers
170 views

Morphing Hypercubes, Token Sliding and Odd Permutations

A month ago, I asked the following question math.exchange (https://math.stackexchange.com/questions/3127874/morphing-hypercubes-and-odd-permutations), but for completeness, I will include the details ...
1
vote
0answers
160 views

Travelling Salesman problem using Guided Local Search

I am doing Week_4 of https://www.coursera.org/learn/discrete-optimization/ stuck in solving TSP. As there are a lot of methods to solve this problem, I am currently coding Guided Local Search as ...
1
vote
1answer
46 views

How to perform local search to find maximal induced subgraphs?

I'm looking for efficient ways to perform local search to find maximal induced subgraphs that satisfy certain properties : a tree, a forest or a bipartite subgraph for example. What I mean by local ...
1
vote
1answer
451 views

Nearest Insertion Traveling Salesman Heuristic: is it faster to insert nearest nodes first?

I am trying to implement the nearest insertion TSP heuristic. However, I am wondering if it matters which node I insert into the subgraph first. For example, should I start with one node; calculate ...
1
vote
1answer
544 views

A* Search Algorithm Implementation with Priority Queue

I've got a question regarding the A* search algorithm's implementation. According to Wikipedia, one has to use a priority queue for retrieving the next node with the lowest f value, is it possible to ...
1
vote
0answers
84 views

Comparison of time-dependent traveling salesman heuristics

I'm looking into implementing a heuristic for the time-dependent traveling traveling salesman problem (TDTSP) that completes in a certain amount of time. There are a wide range of possible ways to ...
1
vote
0answers
212 views

Prove that a convex combination of admissible heuristics is admissible

I got this question that's been troubling me for some time. If $h_1$ and $h_2$ are admissible heuristic functions, prove that $h_3 = (c-1)\,h_1 + c\,h_2$, $0 < c < 1$, is also an admissible ...
1
vote
0answers
96 views

Was the “cuckoo search” independently discovered before 2009? If so, what was the name given to it?

Background: I would like to experiment with evolutionary algorithms to generate the "optimal" poem, according to a fitness function to be determined later. However, I cannot think of a good way of ...
1
vote
0answers
65 views

Difference between Memetic and Cultural algorithms

What is the difference between a memetic algorithm and a cultural algorithm? I mean they're both evolutionary algorithms where they select a subset of the population to apply some local search logic. ...
1
vote
1answer
109 views

Is there any good way to judge whether the rectangle is inside the point cloud? [closed]

How to judge whether a rectangle in the figure is inside the given point cloud? For example, in this figure, the red rectangle is outside the point cloud and the green rectangle is outside the point ...
1
vote
0answers
90 views

Neighbourhood design in Variable Neighbourhood Search

Variable Neighbourhood Search (VNS) is a metaheuristic for solving (combinatorial) optimization problems. It iteratively explores growing neighbourhoods to find better local optima in each iteration. ...
1
vote
0answers
85 views

RINS: start - incumbent and relaxation solution have all different values

RINS: Relaxation induced neighborhood search, firstly introduced by Danna et.al in 2004 in "Exploring relaxation induced neighborhoods to improve MIP solutions" I wanted to design an example how the ...
1
vote
0answers
14 views

Symmetric Roles of the two problem solutions in RINS

Currently, I am reading the paper "Exploring relaxation induced neighborhood to improve MIP solutions" by Danna et.al. from 2004 and they are talking about a symmetric role of incumbent and the ...
1
vote
0answers
116 views

Does the vehicle routing problem and variations have approximation ratios or a PTAS?

This is a somewhat big question since there are many variations on the VRP. The most studied seems to be the capacitated version, the CVRP, but variations considering time windows, backhaul/linehaul, ...
1
vote
0answers
66 views

TSP heuristics for limited distance information [closed]

this is my first question on ComputerScience beta. :) I've posted a similiar question on Mathoverflow and a friendly user advised me to post my question on this site. Problem: I'm looking for ...
1
vote
1answer
63 views

Is there a way to predict rendering times? [closed]

In purpose of load balancing I need to approximatively predict rendering time my graphics software (in the specific case it's Autodesk Maya) needs to render a task given an input file (.ma/.mb) and ...
1
vote
0answers
828 views

Improving MSE as fitness function for a genetic algorithm

I am implementing an autoencoder neural network in matlab, the weights of which are being optimised by a genetic algorithm. At the moment I am working on the first layer, trying to get an improved ...
1
vote
0answers
53 views

A heuristic for finding a disjoint set of representatives

This is my problem: ...
0
votes
2answers
97 views

Greedy Heuristic for the Traveling Salesperson Problem

We're studying Heuristic in my Theoretical CS class, more specifically Greedy-Algorithms for the Traveling Salesperson Problem. The first one is the "next neighbor heuristic", where you start at any ...
0
votes
1answer
1k views

Longest Path A*, Admissible Heuristics, and Optimalness

Im working on a modified A Star algorithm, that instead of attempting to find the shortest path, it tries to find the longest past, or in my specific case, the highest weighted path. I have some ...
0
votes
1answer
65 views

Hueristic Algorithm to find the maximum clique

Let the algorithm be defined as follows: Consider the following heuristic algorithm for finding the maximum size clique in a graph. (1). Delete from the graph a vertex that is not connected to every ...
0
votes
1answer
2k views

Prove consistency of maximum of two consistent heuristic functions?

Suppose we have two heuristic functions $h_1$ and $h_2$ which are both consistent, that is, $$h_i(n) \leq c(n,a,n') + h_i(n')\qquad \ i\in\{1,2\}\,,$$ where $c(n,a,n')$ denotes cost of reaching the ...
0
votes
1answer
176 views

Heuristic function

Is there any way to prove that an admissible heuristic may not be consistent? Most proof I came across are through examples .Is there a generalized proof?